Question

after allowing two successive discounts of 25% and 30% a shopkeeper sells a woolen jacket for Rs.420.find the marked Price of jacket

Answer 1

Given,

After allowing two successive discounts of 25% and 30% a shopkeeper sells a woollen jacket for Rs.420.

To Find,

The marked price of the jacket =?

Solution,

We can solve the question as follows:

It is given that a shopkeeper sold a woollen jacket for two successive discounts of 25% and 30% The final cost of the jacket is Rs. 480. We have to find the marked price.

Let the marked price of the jacket = $x$

Price of the jacket after the first discount:

We can use the formula,

Final price = Original price x (100 - Discount)/100

                 $= x*\frac{100 - 25}{100}$

                 $= x*\frac{75}{100}$

                  $= \frac{3}{4}x$

Now,

Price of the jacket after the second discount:

Now, the new price of the jacket is $\frac{3}{4} x$ and the final price is Rs. 420.

Final price = Original price x (100 - Discount)/100

           $420$ $= \frac{3}{4}x*\frac{100 - 30}{100}$

           $420 = \frac{3}{4} x * \frac{70}{100}$

           $420 = \frac{3}{4} x * \frac{7}{10}$

           $420 = \frac{21}{40}x$

             $x = 420*\frac{40}{21}$

             $x = 800$

Hence, the marked price of the jacket is Rs. 800.

Answer 2

The marked price of the jacket is Rs. 800.

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Let's understand a few concepts:

We will use the following formulas to solve the given problem:

1). If the first discount is x% and the second discount is y% then the total discount in this case of successive discounts is:

$\boxed{\bold{Total \:discount \:percentage= \bigg(x + y - \frac{xy}{100}\bigg)\% }}$

2). The amount of discount will be:

$\boxed{\bold{Discount = \frac{Discount\%}{100} \times M.P.}}$

3). The sale price will be:

$\boxed{\bold{S.P. = M.P. - Discount}}$

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Let's solve the given problem:

The two successive discounts given on the woollen jacket are 25% and 30%

∴ Total discount %

= $\bigg(25 + 30 - \frac{25 \times 30}{100}\bigg)\%$

= $\bigg(55 - \frac{750}{100}\bigg)\%$

= $\bigg(55 - 7.5\bigg)\%$

= $\bigg(47.5\bigg)\%$

The final selling price of the woollen jacket = Rs. 420

Let Rs. "x" be the marked price of the woollen jacket.

Now, by combining the two formulas in 2) and 3), we get

$S.P. = M.P. - \frac{Discount\%}{100} \times M.P.$

$\implies 420 = x - \frac{47.5}{100} \timesx$

$\implies 420 = x - 0.475x$

$\implies 420 = 0.525x$

$\implies \bold{x = 800}$

Thus, the marked price of the woollen jacket is Rs. 800.

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